GATE 2023 CH – Question 65
Pumps $A$ and $B$ are being considered for purchase in a chemical plant. Cost details for these two pumps are given in the table below. The interest rate is 10% per annum, compounded annually. For both the pumps to have the same capitalized cost, the salvage value (in Rs.) of pump B should be ______ (rounded off to the nearest integer).
| Item | Pump $A$ | Pump $B$ |
|---|---|---|
| Installed cost (Rs.) | 16000 | 32000 |
| Uniform end of year maintenance (Rs.) | 2400 | 1600 |
| Salvage value (Rs.) | 1000 | ? |
| Service life (year(s)) | 1 | 2 |
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Show answer and explanation
Correct answer: 2180
Explanation
The capitalised costs are equal when the equivalent annual costs are equal, with the capital recovery factor $\frac{i(1 + i)^n}{(1 + i)^n - 1}$ and the salvage credited as $S \times$ (sinking fund factor) in the annual cost. For pump A (1 year): $(16000 - 1000)(1.1) + 1000(0.1) + 2400 = 16600 + 2400 = 19000$. For pump B (2 years), with $A/P = 0.57619$: $(32000 - S)(0.57619) + 0.1S + 1600 = 18438 - 0.47619S + 1600$. Setting this equal to 19000 gives $0.47619S = 1038$, so $S = 2180$ rupees.